Fracture analysis of linear viscoelastic materials using triangular enriched crack tip elements

A new triangular enriched singular element model is established for the planar fracture problems of linear viscoelastic materials by enriching the viscoelastic asymptotic displacement fields to manifest the singularity at the crack tip. The corresponding triangular transition element is formulated to join the singular elements and common elements in order to eliminate displacement field incompatibility. The viscoelastic incremental formulations of the enriched finite element method in time domain are derived according to the Boltzmann superposition principle. The deformations of crack opening and sliding displacements in the cracked viscoelastic body are numerically investigated and the strain energy release rate is obtained based on the enriched degree of freedoms. The numerical examples show that the results of this present method are very good agreement with the analytical solutions using a relatively coarse meshing and indicate that this present method is accurate and efficient.